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Question

The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm & 34 cm, the distance between their centers is ____ cm.


A

30

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B
28
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C
24
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D
32
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Solution

The correct option is B 28

The perpendicular drawn from centre of the circle bisects the chord.
OO' bisects the chord AB into two equal parts of 15 cm each.
AC = CB = 15cm

Now applying Pythagoras theorem to ΔOAC, we get

(25)2 = (15)2 + (x)2

625 = 225 + (x)2

x = 20 cm

Now, applying Pythagoras theorem in ΔO'AC we get,

(17)2 = (15)2 + (y)2

289 = 225 + (y)2

y = 8 cm

Therefore distance between the two centres is (x+y)=(20+8)=28 cm.


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